Control.Invertible.MonadArrow

A symmetric version of the Kleisli monad transformer arrow. BiKleisli provides this Kleisli-like arrow over bijections.

The Alimarine paper just calls it "MoT" for Monad Transformer.

Documentation

newtype MonadArrow a m b c

Bidirectional Kleisli-like monad arrow transformer.

Constructors

MonadArrow

Fields

• runMonadArrow :: a (m b) (m c)

Instances

Category * a => Category * (MonadArrow a m)

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

Groupoid * a => Groupoid * (MonadArrow a m)

Methods

inv :: k1 a b -> k1 b a

Semigroupoid * a => Semigroupoid * (MonadArrow a m)

Methods

o :: c j k1 -> c i j -> c i k1

Monad m => Arrow (MonadArrow (->) m)

Methods

arr :: (b -> c) -> MonadArrow (->) m b c

first :: MonadArrow (->) m b c -> MonadArrow (->) m (b, d) (c, d)

second :: MonadArrow (->) m b c -> MonadArrow (->) m (d, b) (d, c)

(***) :: MonadArrow (->) m b c -> MonadArrow (->) m b' c' -> MonadArrow (->) m (b, b') (c, c')

(&&&) :: MonadArrow (->) m b c -> MonadArrow (->) m b c' -> MonadArrow (->) m b (c, c')

Monad m => Arrow (MonadArrow (<->) m)

Methods

arr :: (b -> c) -> MonadArrow (<->) m b c

first :: MonadArrow (<->) m b c -> MonadArrow (<->) m (b, d) (c, d)

second :: MonadArrow (<->) m b c -> MonadArrow (<->) m (d, b) (d, c)

(***) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b' c' -> MonadArrow (<->) m (b, b') (c, c')

(&&&) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b c' -> MonadArrow (<->) m b (c, c')

Monad m => ArrowChoice (MonadArrow (->) m)

Methods

left :: MonadArrow (->) m b c -> MonadArrow (->) m (Either b d) (Either c d)

right :: MonadArrow (->) m b c -> MonadArrow (->) m (Either d b) (Either d c)

(+++) :: MonadArrow (->) m b c -> MonadArrow (->) m b' c' -> MonadArrow (->) m (Either b b') (Either c c')

(|||) :: MonadArrow (->) m b d -> MonadArrow (->) m c d -> MonadArrow (->) m (Either b c) d

Monad m => ArrowChoice (MonadArrow (<->) m)

Methods

left :: MonadArrow (<->) m b c -> MonadArrow (<->) m (Either b d) (Either c d)

right :: MonadArrow (<->) m b c -> MonadArrow (<->) m (Either d b) (Either d c)

(+++) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b' c' -> MonadArrow (<->) m (Either b b') (Either c c')

(|||) :: MonadArrow (<->) m b d -> MonadArrow (<->) m c d -> MonadArrow (<->) m (Either b c) d

MonadPlus m => ArrowZero (MonadArrow (->) m)

Methods

zeroArrow :: MonadArrow (->) m b c

MonadPlus m => ArrowZero (MonadArrow (<->) m)

Methods

zeroArrow :: MonadArrow (<->) m b c

MonadPlus m => ArrowPlus (MonadArrow (->) m)

Methods

(<+>) :: MonadArrow (->) m b c -> MonadArrow (->) m b c -> MonadArrow (->) m b c

MonadPlus m => ArrowPlus (MonadArrow (<->) m)

Methods

(<+>) :: MonadArrow (<->) m b c -> MonadArrow (<->) m b c -> MonadArrow (<->) m b c

Monad m => BiArrow' (MonadArrow (<->) m)

(BiArrow a, Monad m) => BiArrow (MonadArrow a m)

Methods

(<->) :: (b -> c) -> (c -> b) -> MonadArrow a m b c

invert :: MonadArrow a m b c -> MonadArrow a m c b

type BiKleisli m a b = MonadArrow (<->) m a b

A MonadArrow over bijections.